%run ../initscript.py
HTML("""
<div id="popup" style="padding-bottom:5px; display:none;">
    <div>Enter Password:</div>
    <input id="password" type="password"/>
    <button onclick="done()" style="border-radius: 12px;">Submit</button>
</div>
<button onclick="unlock()" style="border-radius: 12px;">Unclock</button>
<a href="#" onclick="code_toggle(this); return false;">show code</a>
""")

Enter Password:

Submit

Unclock show code

%run loadtsfuncs.py
from ipywidgets import *
%matplotlib inline
import warnings
warnings.filterwarnings('ignore')
toggle()

show code

Exponential Smoothing Forecasts

The level \(\alpha \in [0,1]\). If you want the method to react quickly to movements in the series, you should choose a large \(\alpha\); otherwise a small \(\alpha\).

• If \(\alpha\) is close to 0, observations from the distant past continue to have a large influence on the next forecast. This means that the graph of the forecasts will be relatively smooth.

• If \(\alpha\) is close to 1, only very recent observations have much influence on the next forecast. In this case, forecasts react quickly to sudden changes in the series.

Simple Exponential Smoothing

widgets.interact_manual.opts['manual_name'] = 'Run Forecast'
interact_manual(ses_forecast,
         forecasts=widgets.BoundedIntText(value=12, min=1, description='Forecasts:', disabled=False),
         holdouts=widgets.BoundedIntText(value=0, min=0, description='Holdouts:', disabled=False),
         level=widgets.BoundedFloatText(value=0.2, min=0, max=1, step=0.05, description='Level:', disabled=False),
         optimized=widgets.Checkbox(value=False, description='Optimize Parameters', disabled=False))
plt.show()

Holt’s Model for Trend

The new smoothing constant \(\beta\) controls how quickly the method reacts to observed changes in the trend.

• If \(\beta\) is small, the method reacts slowly,

• If \(\beta\) is large, the method reacts more quickly.

Some practitioners suggest using a small value of \(\alpha\) (such as 0.1 to 0.2) and setting \(\beta = \alpha\). Others suggest using an optimization option to select the optimal smoothing constant.

from statsmodels.tsa.holtwinters import Holt

# df_house.index.freq = 'MS'
plt.figure(figsize=(12, 6))
train = df_house.iloc[:, 0]
train.index = pd.DatetimeIndex(train.index.values, freq=train.index.inferred_freq)
model = Holt(train).fit(smoothing_level=0.2, smoothing_slope=0.2, optimized=False)
pred = model.predict(start=train.index[0], end=train.index[-1] + 12*train.index.freq)

plt.plot(train.index, train, label='Train', c='cornflowerblue')
plt.plot(pred.index, pred, label='Holt\'s', c='orange')
plt.legend(loc='best')
plt.title('House Sales')
plt.show()

toggle()

show code

Winters’ Exponential Smoothing Model

from statsmodels.tsa.holtwinters import ExponentialSmoothing

plt.figure(figsize=(12, 6))
train, test = df_drink.iloc[:-8, 0], df_drink.iloc[-8:,0]
train.index = pd.DatetimeIndex(train.index.values, freq=train.index.inferred_freq)

model = ExponentialSmoothing(train, seasonal='mul', seasonal_periods=4).fit(smoothing_level=0.2,
                                        smoothing_slope=0.2,
                                        smoothing_seasonal=0.4,
                                        optimized=False)
pred = model.predict(start=train.index[0], end=test.index[-1] + 4*train.index.freq)

plt.plot(train.index, train, label='Train', c='cornflowerblue')
plt.plot(test.index, test, label='Holdouts', c='fuchsia')
plt.plot(pred.index, pred, label='Winters\'', c='orange')
plt.legend(loc='best')
plt.title('Drink Sales')
plt.show()

toggle()

show code